Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 10
... internally and C ' to divide it externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of ...
... internally and C ' to divide it externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of ...
Page 13
... internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- point , by what name will you call the distance between their ...
... internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- point , by what name will you call the distance between their ...
Page 20
... internal bisector , and the one lying without is the external bisector . B Ό F D A Let AOC be a given angle ; and let EOF be so drawn that LAOE = LEOC . EF is the internal bisector of the angle AOC . Also , let GOH be so drawn that LCOG ...
... internal bisector , and the one lying without is the external bisector . B Ό F D A Let AOC be a given angle ; and let EOF be so drawn that LAOE = LEOC . EF is the internal bisector of the angle AOC . Also , let GOH be so drawn that LCOG ...
Page 21
Nathan Fellowes Dupuis. and the external bisector of AOC is the internal bisector of its supplementary angle , COB ... internally , and the other externally . Thus , if OE is so drawn that the LAOE is double the LEOC , some line OG may ...
Nathan Fellowes Dupuis. and the external bisector of AOC is the internal bisector of its supplementary angle , COB ... internally , and the other externally . Thus , if OE is so drawn that the LAOE is double the LEOC , some line OG may ...
Page 24
... internal angle , while the angles CAB and ABC are opposite internal angles . 4. Any side of a triangle may be taken as its base , and then the angles at the extremities of the base are its basal angles , and the angle opposite the base ...
... internal angle , while the angles CAB and ABC are opposite internal angles . 4. Any side of a triangle may be taken as its base , and then the angles at the extremities of the base are its basal angles , and the angle opposite the base ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices